Related papers: Covariance matrices of self-affine measures

We conduct the multifractal analysis of self-affine measures for "almost all" family of affine maps. Besides partially extending Falconer's formula of $L^q$-spectrum outside the range $1< q\leq 2$, the multifractal formalism is also…

A coprime array receiver processes a collection of received-signal snapshots to estimate the autocorrelation matrix of a larger (virtual) uniform linear array, known as coarray. By the received-signal model, this matrix has to be (i)…

We establish matrix representations for self-similar measures on $\mathbb{R}^d$ generated by equicontractive IFSs satisfying the finite type condition. As an application, we prove that the $L^q$-spectrum of every such self-similar measure…

In this self-contained chapter, we revisit a fundamental problem of multivariate statistics: estimating covariance matrices from finitely many independent samples. Based on massive Multiple-Input Multiple-Output (MIMO) systems we illustrate…

Sparse covariance matrices play crucial roles by encoding the interdependencies between variables in numerous fields such as genetics and neuroscience. Despite substantial studies on sparse covariance matrices, existing methods face several…

In this paper we construct the new coefficient which allows to measure quantitatively the independence of the two discrete random variables. The new inequalities for the matrices with non-negative elements are found

We develop a method for estimating well-conditioned and sparse covariance and inverse covariance matrices from a sample of vectors drawn from a sub-gaussian distribution in high dimensional setting. The proposed estimators are obtained by…

We gather several results on the eigenvalues of the spatial sign covariance matrix of an elliptical distribution. It is shown that the eigenvalues are a one-to-one function of the eigenvalues of the shape matrix and that they are closer…

Covariance matrices are important tools for obtaining reliable parameter constraints. Advancements in cosmological surveys lead to larger data vectors and, consequently, increasingly complex covariance matrices, whose number of elements…

The accurate computation of the covariance matrix of fitted model parameters is a somewhat neglected task in Statistics. Algorithms are given for computing accurate covariance matrices derived from computing the Hessian matrix by numerical…

We introduce a new set of algorithms to compute Jacobi matrices associated with measures generated by infinite systems of iterated functions. We demonstrate their relevance in the study of theoretical problems, such as the continuity of…

We derive tight lower bounds on the smallest eigenvalue of a sample covariance matrix of a centred isotropic random vector under weak or no assumptions on its components.

Let $M_n$ be a $n \times n$ Wigner or sample covariance random matrix, and let $\mu_1(M_n), \mu_2(M_n), ..., \mu_n(M_n)$ denote the unordered eigenvalues of $M_n$. We study the fluctuations of the partial linear eigenvalue statistics $$…

Building upon earlier work in which axioms were formulated for multivariate measures of concordance, we examine properties of such measures. In particular, we examine the relations between the measure of concordance of an $n$-copula and the…

In this work, we give a variation of parameters formula for nonautonomous linear impulsive differential equations with piecewise constant arguments of generalized type. We cover several cases of differential equations with deviated…

We prove an abstract instability result for an eigenvalue problem with parameter. We apply this criterion to show the transverse linear instability of solitary waves on various examples from mathematical physics.

This paper gives a review of the recent progress in the study of Fourier bases and Fourier frames on self-affine measures. In particular, we emphasize the new matrix analysis approach for checking the completeness of a mutually orthogonal…

We extend the results about the fluctuations of the matrix entries of regular functions of Wigner matrices to the case of sample covariance random matrices.

We propose a formula expressing Perron - Frobenius eigenvectors of Cartan matrices in terms of products of values of the Gamma function.

We extend to the matrix setting a recent result of Srivastava-Vershynin about estimating the covariance matrix of a random vector. The result can be in- terpreted as a quantified version of the law of large numbers for positive…